電大西方經(jīng)濟(jì)學(xué)計(jì)算題小抄參考

1、專業(yè)好文檔1、已知某商品的需求方程和供給方程分別為：qd=14-3p，qs=2+6p，試求：該商品的均衡價(jià)格，以及均衡時的需求價(jià)格彈性和供給價(jià)格彈性。解：（1）均衡時，供給量等于需求量，即qd=qs，也就是 14-3p=2+6p解得 p=4/3 ，q=10 。 （2）需求價(jià)格彈性：ed=-qd/qp/p=-qd/pp/q=-(-3) 4/3/10= 4/10 = 0.4 需求供給彈性：ed=qs/qp/p=qs/pp/q=6 4/3/10 = 4/5=0.8 2、若消費(fèi)者張某的收入為270元，他在商品x和y的無差異曲線上斜率為dy/dx=-20/y的點(diǎn)上實(shí)現(xiàn)均衡。已知x和y的價(jià)格分別為px=2

2、，py=5，那么此時張某將消費(fèi)x和y各多少?解:消費(fèi)者均衡條件為：- dy/dx = mrs = px/py，所以-(-20/y)= 2/5，y = 50。根據(jù)收入i= xpx+ypy，可以得出：270=x2 + 505，x=10，則消費(fèi)者消費(fèi)10單位x和50單位y。 3、若消費(fèi)者張某消費(fèi)x和y兩種商品的效用函數(shù)u=x2y2，張某收入為500元，x和y的價(jià)格分別為px =2元，py=5元，求: (1)張某的消費(fèi)均衡組合點(diǎn)。解:由效用函數(shù)u=x2y2，可得m ux= 2xy2，m uy = 2x2y，消費(fèi)者均衡條件為：m ux / m uy =2 xy2/ 2x2y =y/x=px/py= 2/

3、5，500 = 2x+5y，可得，x=125，y=50，即張某消費(fèi)125單位x和50單位y時，達(dá)到消費(fèi)者均衡。 (2)若政府給予消費(fèi)者消費(fèi)x以價(jià)格補(bǔ)貼，即消費(fèi)者可以原價(jià)格的50%購買x，則張某將消費(fèi)x和y各多少?解:消費(fèi)者可以原價(jià)格的50%購買x，意味著商品x的價(jià)格發(fā)生變動，預(yù)算約束線隨之變動。消費(fèi)者均衡條件成為:y/x = 1/5，500=lx+5y，可得x=250，y=50，張某將消費(fèi)250單位x，50單位y。 (3)若某工會愿意接納張某為會員，會費(fèi)為100元，但張某可以50%的價(jià)格購買x，則張某是否應(yīng)該加入該工會? 解:張某收入發(fā)生變動，預(yù)算約束線也發(fā)生變動。消費(fèi)者均衡條件成為：y/x

4、= 1/5 400 = lx+5y，可得x= 200，y = 40，比較一下張某參加工會前后的效用。參加工會前:u=x2y2 = 1252502=39062500，參加工會后:u=x2y2 = 2002 402=64000000，可見，參加工會以后所獲得的總數(shù)效用較大，所以張某應(yīng)加入工會。 4、假定某完全競爭的行業(yè)中有500家完全相同的廠商，每個廠商的成本函數(shù)為stc=0.5q2 + q + 10。(1)求市場的供給函數(shù)。 (2)假定市場需求函數(shù)為qd= 4000 - 400p，求市場均衡價(jià)格。解: (1)根據(jù)stc = 0.5 q2 + q +10，得avc = 0.5q + 1，則p =

5、q+1為單個廠商的供給函數(shù)，由此可得市場的供給函數(shù)qs = 500p 500。 (2)當(dāng)qd= qs時，市場處于均衡，由4000 - 400p = 500p - 500，得市場均衡價(jià)格為p=5。5、設(shè)有如下簡單經(jīng)濟(jì)模型：c=80+0.75yd，yd=y-t，t=-20+0.2y，i=50+0.1y，g=200，試求：收入、消費(fèi)、投資與稅收的均衡值及綜合乘數(shù)。解：y = c+i+g = 80+0.75y-（-20+0.2y）+50+0.1y+200得到y(tǒng)=1150，c = 80+0.75yd = 785，i = 50+0.1y = 165， t = -20+0.2y = 210，已知c=80+0

6、.75yd，得到b=0.75, 已知t=-20+0.2y，得到 t=0.2, 已知i=50+0.1y，得到邊際儲蓄傾向=0.1 ，k=1/1-（0.750.8+0.1）= 3.3 。 由簡單的國民收入決定模型可知，均衡時有：y=c+i+g=80+0.75yd+50+0.1y+200,因?yàn)閥d=y-t=y-(-20+0.2y)=0.8y+20,所以y=80+0.75(0.8y+20)+50+0.1y+200，0.3y=345,均衡的國民收入為：y=1150。當(dāng)y=1150時有：c=80+0.75yd=80+0.75（0.8y+20）=80+0.75(0.8*1150+20)=785。i=50+0

7、.1y=50+0.1*1150=165，t=-20+0.2y=-20+0.2*1150=210，k=1/1-b(1-t)-i=1/1-0.75(1-0.2)-0.1=3.3。6、設(shè)完全競爭市場中的代表性廠商的短期成本函數(shù)是,若該產(chǎn)品的市場價(jià)格時315元，試問：(1)該廠商利潤最大時的產(chǎn)量和利潤；(2)該廠商的不變成本和可變成本曲線及圖形。 解：（1）因?yàn)閙c= 240 40q + 3q2, mr = 315， 得q=15,利潤 =tr-tc = 2250。 （2）不變成本fc=20,可變成本vc = 240q 20q2 + q3 ,依據(jù)兩個方程畫出不變成本和可變成本曲線： （3）停止?fàn)I業(yè)點(diǎn)應(yīng)該

8、是平均變動成本的最低點(diǎn)，所以avc=vc/q=(240q-20q2+q3)/q=240-20q+q2，對avc求導(dǎo)，得：q=10 此時avc=140，停止?fàn)I業(yè)點(diǎn)時價(jià)格與平均變動成本相等，所以只要價(jià)格小于140，廠商就會停止?fàn)I。(4）該廠商的供給曲線應(yīng)該是產(chǎn)量大于10以上的邊際成本曲線7、已知：邊際消費(fèi)傾向?yàn)?.8，邊際稅收傾向?yàn)?.15，政府購買支出和轉(zhuǎn)移支付各增加500億元。試求：(1)政府購買支出乘數(shù)；(2)轉(zhuǎn)移支付乘數(shù)；(3)政府支出增加引起國民收入增加顫；(4)轉(zhuǎn)移支付增加引起的國民收入增加額。 解：已知b=0.8 t=0.15 c500 政府轉(zhuǎn)移支付，tr=500， (1)kg=1/

9、1-b(1-t)=1/1-0.8*(1-0.15）=3.1， (2)ktr=b/1-b(1-t)=0.8/1-0.8*(1-0.15)=2.5,(3)yg=gkg=5003.1=1550，(4)ytr=trktr=5002.5=1250， 8、已知q=675050p，總成本函數(shù)為tc=12000+o.025q2。 求: (1)利潤最大時的產(chǎn)量和價(jià)格?(2)最大利潤是多少?解：已知q=675050p，總成本函數(shù)為tc=12000+o.025q2，得到p=135-q/50 。mc= 0.05q ，tr=pq=135q-q2/50，mr=135-q/25，根據(jù) mc=mr,得到 0.05q=135-

10、q/25 ，q=1500，p=135-q/50= 105，利潤= tr-tc= pq-(12000+o.025q2)= 89250 。9、設(shè)有下列經(jīng)濟(jì)模型：y=c+i+g，i=20+o.15y，c=40+0.65y，g=60。試求： (1)邊際消費(fèi)傾向及邊際儲蓄傾向各為多少?(2)y，c，i的均衡值； (3)投資乘數(shù)為多少。 解：(1)由已知c=40+0.65y，得到邊際消費(fèi)傾向b=0.65，邊際儲蓄傾向=1-邊際消費(fèi)傾向=1-0.65=0.35。(2) y=c+i+g=40+0.65y+20+0.15y+60，得到y(tǒng)=600，c=40+0.65，y=430，i=20+0.15y=110，(3

11、) k=1/1-(0.15+0.65)=5 。 10、某鋼鐵廠的生產(chǎn)函數(shù)為q=5lk，其中q為該廠的產(chǎn)量，l為該廠每期使用的資本數(shù)量，k為該廠每期使用的資本數(shù)量。如果每單位資本和勞動力的價(jià)格分別為2元和1元，那么每期生產(chǎn)40單位的產(chǎn)品，該如何組織生產(chǎn)?解:由該廠的生產(chǎn)函數(shù)q=5lk可得，m pl= 5k，mpk= 5l，按照廠商組合生產(chǎn)的最優(yōu)要素組合可得出5k/5l=1/2（1），又由廠商每期生產(chǎn)20單位產(chǎn)品的條件可知40=4lk（2），由(1)(2)可求出k=2，l=4，即生產(chǎn)者應(yīng)該購 買資本2個單位，購買勞動力4個單位，進(jìn)行生產(chǎn)。 11、已知貨幣供給量m220，貨幣需求方程為l0.4y1.

12、2r，投資函數(shù)為i1952000r， 儲蓄函數(shù)為s500.25y。設(shè)價(jià)格水平p1，求均衡的收入水平和利率水平。 解:由產(chǎn)品市場均衡條件is，1952000r500.25y，0.25y2000r245（1），由貨幣市場均衡條件：lmp，0.4y1.2r220（2），由(1) (2)兩式有方程組y500，r0.06，即均衡的收入水平為500，均衡的利率水平為0.06。winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after

13、a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the o

14、pening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi

15、 - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air

16、 up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, h

17、e told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has

18、also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could

19、happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmos

20、phere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer

21、(called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will n

22、ot make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on the